The present invention relates to computer generated holograms, and, more particularly, to a method for encoding holograms using only phase.
Holography has always played a major role in the optical data processing field. Traditionally, the recorded complex functions were modulated by a carrier frequency and reconstructed in the first diffraction order (off-axis holography). The flexibility of this method was extremely restricted: Only functions with real impulse response could be generated. The generation of an arbitrary complex function seemed to be far from being realized. The needed flexibility was primarily introduced by Brown and Lohmann (G. R. Brown and A. W. Lohmann (1966), "Complex spatial filtering with binary masks", Applied Optics vol. 6 pp. 967-969), and by Lohmann and Paris (A. W. Lohmann and D. P. Paris (1967), "Binary Fraunhofer holograms generated by computer", Applied Optics vol. 6 pp. 1739-1749), who invented the first computerized encoding method. The holograms generated by this approach were binary, allowing the production of an arbitrary function distribution, and were rapidly generated by a computer. In this approach the Fourier transform of the image desired to be reconstructed was divided into pixels. The amplitude of each filter pixel was encoded by plotting a binary square inside the region of the corresponding hologram pixel. The area (or the cosine of the area) of the plotted square is proportional to the amplitude to be encoded in this pixel. In order to encode the phase, the central location of the square was proportionally shifted from the central location of the pixel's region. The reconstructed image was obtained in the first diffraction order.
In many applications, the wavefronts to be recorded in the holograms have only phase variations. When these wavefronts are recorded as image holograms, they are similar to interferograms. Later on, modified ways of encoding were suggested. An explanation of some of these methods was published by Lee (W. H. Lee (1978), "Computer generated holograms: techniques and applications,", in Progress in Optics, vol. 16 (E. Wolf, ed.) pp. 119-132), and experimental comparison between them was performed by Han and Casasent (C. W. Han and D. P. Casaent (1988), "Experimental comparison of computer generated holograms", Proc. SPIE, vol. 884 pp. 72-80). In each approach, a different mathematical relation connected the location of the square and the area of the square, and the amplitude and the phase that are encoded in the pixel. The common principle of all of those methods is that the reconstructed image is obtained in the first diffraction order. Recently, a method of encoding two functions simultaneously was suggested (D. Mendelovic and I. Kiryuschev (1995), "Two channel computer-generated hologram and its application for optical correlation", Optical Communication vol. 116 pp. 322-325) Here, the two different images are reconstructed in the two orthogonal different first orders.
The main disadvantage of obtaining a reconstruction in the first diffraction order is that the quality of the reconstruction is highly dependent upon the wavelength of illumination. If deviations of the wavelength .lambda. occur in the illuminating source, as often happens in the case of practical optical systems and light sources, the quality of reconstruction rapidly decreases, at a rate dependent upon the amount of deviation. Moreover, working in the first diffraction order increases the complexity of the system and often decreases significantly the light efficiency of the system.
There is thus a widely recognized need for, and it would be highly advantageous to have, a method for generating zero diffraction order holograms by computer.